Abstract Algebra

• Algebraic Structures:
  • groups
  • rings, modules
  • fields, vector spaces
  • group-theoretic lattices, and order-theoretic lattices

Number Theory

• numbers, integers
• integer partition

Category Theory

• category

Combinatorics

• permutations, derangements, combinations

Set Theory

• sets, set partitions,
• functions, and relations

Graph Theory

• graphs, trees, nodes, edges

Geometry

• points, lines, line segments
• polytopes:
  • polygons (triangles, squares, pentagons, hexagons, etc)
  • polyhedra (tetrahedrons, cubes, octahedrons, dodecahedrons, icosahedrons, etc)
• non-polytopes:
  • non-polygons (circles, ellipses, parabolas, hyperbolas, etc)
  • non-polyhedra (spheres, ellipsoids, paraboloids, hyperboloids, cylinders, cones, etc)

Topology

• topological spaces and manifolds

Linear Algebra

• scalars, vectors, matrices

Other

• expressions